Orca is a passenger ship, works, Dolphin is a passenger ship, works. The Beluga isn't the only ship of it's kind, but the only of all 31 that overheats so badly.
Lets take a look at this, shall we?
Firstly, we'll state the obvious. These are smaller ships with smaller power requirements, therefore, less heat output. Slightly less obvious, is that neither the Orca nor Dolphin are capable of housing an SLF Bay.
Now to cover the less obvious stuff. I decided to use your Beluga Build as a guide to building an Orca. Some Luxury Cabins, some Packhounds, Prismatic shields...
Here's the build so you can take a look for yourself, (Important note is that none of this stuff is engineered, so there's no excess power requirements):
First thing I noticed? 114% Power requirement. So it needs overcharged. 97.1% with hardpoints retracted. I can see this sitting at >60% heat as a base level easily. Then you'll overcharge the powerplant and reduce heat efficiency... I'll leave that one alone.
Next thing is that you require at least 500Mj shields. I put the largest Prismatic Generator on, and got 465Mj. So I'll guess you'll engineer that for heavy duty. Looks like that power requirement and heat output just shot up another few percent...
I had the option of swapping out the Fuel Scoop for a larger one in exchange for one of the cabins. But that would only increase power consumption, that can be edited to suit the pilots patience really. As can the SCB, I only put that there because you have one, but still, it adds to the power and heat.
The thing is I'm semi-confident that this 'un-modded' Orca would permit me to charge my FSD with no issues. When I get the opportunity, I will gladly spend the 100mill necessary to prove it. But I know that it would be close to overheating.
I also know, that I wouldn't dare fly this Orca in Open. An interdiction from any reasonably armed CMDR and I might as well shut off all modules and shake an angry fist for all the effectiveness it would have at protecting me. But then, as you said, you only face NPC Asps ad Dropships, so I feel I'm to glean you stick to PG and Solo with this build? (Nothing wrong with that, just explains why you don't feel the need to counter anything more than that).
The last bit is somewhat irrelevant to the issue at hand of course. The conclusion to draw is simple enough, and I've said it numerous times.
Your Belugas overheating issues are a case of PEBCAK
You've built a ship designed to fight people while others relax in hottubs. Now you're wondering why it cooks itself when you do the one thing in any ship that produces the most heat. I honestly don't know how else to explain it really.
But, before you respond, do me one small favour. Look at your build. Look at it good an hard and ask yourself, "Where is all my thermal efficiency?". You have 5 Engineered Packhounds with reduced thermal load. But everything else you've modified has decreased efficiency and/or increased thermal load.
5 Modules with a base high thermal load, which you've taken steps to reduce.
Plus 15 more modules with various degrees of base heat/power levels, but all engineered in ways that increase one or both of those stats.
Once more: Your ship overheats because of Hubris. You're asking it to do too much. If it could do everything you're asking of it, no other ship would be necessary.
I used a "spam rolled" G1 Low Emission power plant, to get good SC temperatures with a useful amount of power.